A method of adjusting the strength of applied brake with an operator operating a foot brake or a brake lever has hitherto been practiced for the purpose of keeping a vehicle speed at a control target value when a vehicle runs down a slope. In mines or the likes where a downward slope continues over a long distance, however, it is troublesome for the operator to operate the brake whenever an occasion requires. In a downhill speed control system for releasing the operator from the troublesome braking operation in such a case, as disclosed in, e.g., JP-A-6-135260, a target vehicle speed is set depending on a road surface gradient angle detected by a road surface gradient sensor, and a retarder brake is controlled so that a vehicle speed detected by a vehicle speed sensor is held at the target vehicle speed. Further, the disclosed control system includes a loaded weight sensor, and the strength of the applied brake is controlled depending on the amount of earth and sand loaded in a vessel.